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"The previous process for getting started with Tails was very complex and was problematic for less tech-savvy users. It required starting Tails three times, and copying the full ISO image onto a USB stick twice before having a fully functional Tails USB stick with persistence enabled."

You should look at it from the perspective of the target audience. From there this seems to be the first easy to install OS with an emphasis on privacy.

Yeah, that's what it looks like, and I'm not sure I want that on a tails usb stick. Should I want that?

People like to save stuff. But it ought to be securely encrypted stuff. That's a little iffy on flash storage. But hey.

Do the installer download their own version of Debian, or do it use the repositories of the host machine?

You need to provide the Tails ISO, downloaded separately from Tails' website. The installer does not download or reuse anything from host machine.